Proposition 1 ([1]})
Given a sequence of random vectors \(\left\lbrace  \varphi \left( t \right) \right\rbrace  _{t\in \mathbb {Z}_+}\subseteq \mathbb {R}^n\) , we define a network-level summation of random variables by
\( \mathbf {\bar{x}}\left( t+1 \right) =\Pi _{\chi ^n}^{\psi }\left( \sum _{s=1}^t{\varphi \left( s \right)},\alpha \left( t \right) \right). \) 
